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Modules of finite Gorenstein flat dimension and approximations

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  • Ioannis Emmanouil

Abstract

We study approximations of modules of finite Gorenstein flat dimension by (projectively coresolved) Gorenstein flat modules and modules of finite flat dimension. These approximations determine the Gorenstein flat dimension and lead to descriptions of the corresponding relative homological dimensions, for such modules, in more classical terms. We also describe two hereditary Hovey triples on the category of modules of finite Gorenstein flat dimension, whose associated exact structures have homotopy categories equivalent to the stable category of projectively coresolved Gorenstein flat modules and the stable category of cotorsion Gorenstein flat modules, respectively.

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  • Ioannis Emmanouil, 2024. "Modules of finite Gorenstein flat dimension and approximations," Mathematische Nachrichten, Wiley Blackwell, vol. 297(4), pages 1187-1207, April.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:4:p:1187-1207
    DOI: 10.1002/mana.202200555
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    References listed on IDEAS

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    1. Lars Winther Christensen & Sergio Estrada & Peder Thompson, 2021. "Gorenstein weak global dimension is symmetric," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2121-2128, November.
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